Ann. occup. Hyg., Vol. 48, No. 5, pp. 483–490, 2004
© 2004 British Occupational Hygiene Society
Published by Oxford University Press
doi:10.1093/annhyg/meh031
Particle Deposition in Industrial Duct Bends
THOMAS M. PETERS and DAVID LEITH*
Department of Environmental Sciences and Engineering, The University of North Carolina, Chapel Hill,
NC 27599, USA
Received 30 September 2003; in final form 6 January 2004; published online on 7 July 2003
A study of particle deposition in industrial duct bends is presented. Particle deposition by size
was measured by comparing particle size distributions upstream and downstream of bends
that had geometries and flow conditions similar to those used in industrial ventilation. As the
interior surface of the duct bend was greased to prevent particle bounce, the results are applicable to liquid drops and solid particles where duct walls are sticky. Factors investigated were:
(i) flow Reynolds number (Re = 203 000, 36 000); (ii) particle Reynolds number (10 < Rep∞ <
200); (iii) particle Stokes number (0.08 < Stk < 16); (iv) bend angle (θ = 45°, 90°, 180°); (v) bend
curvature ratio (1.7 < R0 < 12); (vi) orientation (horizontal-to-horizontal and horizontal-tovertical); and (vii) construction technique (smooth, gored, segmented). Measured deposition
was compared with models developed for bends in small diameter sampling lines (Re < 20 000;
Rep∞ < 13). Whereas deposition measured in this work generally agreed with that estimated
with models for particles <30 µm (Stk < 0.7), it was significantly lower than that estimated for
larger particles. As the flow around larger particles became increasingly turbulent, the models
progressively under-represented drag forces and over-estimated deposition. For particles
>20 µm, deposition was slightly greater in the horizontal-to-horizontal orientation than in the
horizontal-to-vertical orientation due to gravitational settling. Penetration was not a multiplicative function of bend angle as theory predicts, due to the developing nature of turbulent
flow in bends. Deposition in a smooth bend was similar to that in a gored bend; however, a
tight radius segmented bend (R0 = 1.7) exhibited much lower deposition. For more gradual
bends (3 < R0 < 12), curvature ratio had negligible effect on deposition.
Keywords: bend; elbow; deposition; droplet; duct; impaction; transport; ventilation
that adhere to the duct walls upon impact. Deposited
droplets and particles can restrict airflow in branch
lines, create fire hazards, cause failure of overhead
supports, and present growth media for biological
contaminants (May and Berard, 1987; Gregory et al.,
1991).
This work focuses on particle deposition in industrial duct bends. The objectives are: (i) to measure
deposition in industrial bends; and (ii) to compare
these measurements with estimates from published
models.
INTRODUCTION
Particle deposition in ducts is important in situations
ranging from the pneumatic transport of materials
and icing of aircraft intakes to bioterrorist attacks. In
occupational hygiene, the airflow velocity required to
prevent particle deposition in ducts, commonly called
the criterion of minimum transport velocity, serves as
the basis for exhaust system design (ACGIH, 1998).
Acceptable values for this criterion are available for
solid particles that bounce upon contact with duct
walls and are then re-entrained into the highly turbulent airflow of an industrial exhaust system (Baliff et
al., 1948; DallaValle, 1932; Rajahns and Thompkins,
1967). The criterion of minimum transport velocity is
not suited for liquid particles, especially oil droplets,
BACKGROUND
A bend introduces several scales of curvilinear
motion to duct flow. The largest of these motions
occurs as the bend reorients the direction of the
airflow: its radius is of the size of the bend radius, Rb.
As the centrifugal force drives the central air core
toward the outer wall, a smaller secondary flow
*Author to whom correspondence should be addressed.
Tel: +1-919-966-3851; fax: +1-919-966-7911;
e-mail: [email protected]
483
484
T. M. Peters and D. Leith
develops perpendicular to the main flow. The size of
the secondary flow is of the size of the duct radius, a
(Ito, 1987), and its strength is characterized by the
Dean number, De (Berger and Talbot, 1983): De =
Re/(R0)1/2, where R0 is the radius of the bend divided
by the radius of the duct (R0 = Rb/a), and Re is the
Reynolds number. For laminar flows (De < 370), the
flow rapidly becomes fully developed with a single
pair of counter-rotating vortices (Berger and Talbot,
1983).
For turbulent flows (De > 370), experiments show
that airflow continually develops throughout a 180°
bend (Rowe, 1970; Enayet et al., 1982; Azzola et al.,
1986; Anwer et al., 1989). In this flow regime,
further vortical structures can develop at various
locations in the bend (Boersma and Nieuwstadt,
1996). For tight bends (R0 < 3) with turbulent flow,
separation can occur at the inner wall causing the
replacement of the secondary flow with a single
circulation pattern that switches direction at low
frequency, f (Tunstall and Harvey, 1968). Rütten et
al. (2001) characterized this phenomenon with the
dimensionless Strouhal number: Sr = 2fDduct/U0.
Several mechanisms, including Brownian diffusion, gravitational setting and electrostatic forces, can
cause particles to deposit in ducts. In bends, the
mechanism of inertial impaction dominates deposition for particles >10 µm (Brockmann, 2001). Given
sufficient inertial force, a particle will deviate from
airflow streamlines and hit the bend wall. Deposition
will occur if the adhesive forces are greater than the
rebound forces (Hinds, 1999).
Particle deposition in bends has been characterized with the following dimensionless parameters:
(i) particle Stokes number (Stk = τU0/a); (ii) particle
free-stream Reynolds number (Rep∞ = DpU0/ν);
(iii) flow Reynolds number (Re = DductU0/ν); (iv) De;
and (5) R0 (Cheng and Wang, 1975; Pui et al., 1987).
All researchers have used Stk to describe results, but
use of parameters such as R0 and Re have been
debated (Crane and Evans, 1977; Cheng and Wang,
1981; Pui et al., 1987).
For laminar flows (De < 900; Re < 3000), Tsai
and Pui (1990) claimed increased deposition with
increased secondary flow strength (De high and R0
small) and used Stk, Re, De and R0 to describe their
results. For moderately turbulent flows, Pui et al.
(1987) used Stk alone to describe experimental measurements (R0 = 5.7; Re = 10 000 and 6000; and Rep∞
< 13) as: ηdep = (1–10–0.963 Stk) × 100%. Brockmann
(1993) modified this formula to include the bend
angle in radians (θ):
η dep = [ 1 – exp ( – 1.412Stkθ ) ] × 100%
(1)
McFarland et al. (1997) used Stk, θ and R0 to
describe the fraction of particles penetrating a bend.
Their correlation can be rewritten in terms of deposition as:


4.61 + a m θStk
-
η dep = 100% – exp  --------------------------------------------------------------------------------2
2
 1 + b m θStk + c m θStk + d m θ Stk
(2)
where, am, bm, cm and dm are coefficients found using
a curve-fitting program. However, an error appears in
the published coefficient for the second term in the
numerator of coefficient dm. Equation (13) of McFarland et al. (1997) should read:
a m = – 0.9526 – 0.05686R 0
– 0.297 – 0.0174R 0
b m = -----------------------------------------------------2
1 – 0.07R 0 + 0.0171R 0
(3)
1.895 2.0
c m = – 0.306 + ------------- – ------R0 R0
2
0.131 – 0.0132R 0 + 0.000383R 0
d m = ----------------------------------------------------------------------------2
1 – 0.129R 0 + 0.0136R 0
For highly turbulent flow, Hacker et al. (1953)
investigated deposition of water drops entering
aircraft intakes (700 000 < Re < 3 700 000). Using a
two-dimensional potential flow simulation, they
demonstrated that Rep∞ strongly influenced deposition. Crane and Evans (1977) suggested that Rep∞
could affect deposition to a greater extent than R0.
Their analysis estimated that for Stk = 0.7 and R0 = 4
deposition would decrease from 58% for Rep∞ of 0, to
52% for Rep∞ of 5, and to 26% for Rep∞ of 450.
In industrial ventilation ducts, recommended
minimum transport velocity ranges from 10 m/s for
welding fumes to 30 m/s for heavy or moist dusts
(Alden and Kane, 1982). Given a transport velocity
of 20 m/s, the flow Re increases from 130 000 to
1 300 000 as the diameter of industrial duct increases
from 0.1 m to 1 m. Typical values of R0 are between
3 and 5; cost factors generally limit the use of bends
with large R0, and high pressure drop prevents widespread use of bends with small R0 (ACGIH, 1998).
Given these restrictions, De in industry is ~30 000–
500 000. For droplets of unit density, Stk ranges from
0.01 to 4, and Rep∞ ranges from 1 to 300 for particles
of 10–100 µm, respectively.
Previous work is inadequate to describe particle
behavior in industrial bends. The correlation models
of Pui et al. (1987) and McFarland et al. (1997) were
constructed using experimental data atypical of
industry: i.e. small particles (Dp < 10 µm), small
diameter tubes (Dduct < 1.6 cm), and moderately turbulent flow (Re < 19 000). The theoretical studies of
Hacker et al. (1953) and Crane and Evans (1977) are
useful in a qualitative sense, but are difficult to apply
to a new set of conditions and have no experimental
Particle deposition in industrial bends
backing. Moreover, past research has been limited to
bends with smooth interior walls, when, in reality, the
interior of industrial bends is rarely smooth because
of the manner in which they are constructed. Thus,
the experiments presented in the current work are the
first to be directly applicable to industrial bends.
MATERIALS AND METHODS
Particle deposition
Particle deposition by size was measured using the
methods presented by Peters and Leith (2003); a brief
overview of this method is provided here. Figure 1
illustrates the experimental set-up. Upstream of the
test bend, an aerosol generator introduced polydisperse glass spheres that ranged in size from 5 to
150 µm. To capture and retain particles that hit the
485
wall, the interior of the bend was coated with petroleum jelly. Circular sampling grids were cut from
welded-wire mesh, coated with petroleum jelly, and
alternately inserted into the duct upstream and downstream of the bend. Upstream velocity profiles were
characteristic of fully developed pipe flow (Tennekes
and Lumley, 1972), and particle profiles were
uniform in concentration and size distribution.
After sampling, the collected particles were recovered from the grids using a hexane extraction
procedure and then sized using a sedimentation
pipette (Silverman et al., 1971). Cumulative mass
distributions were fitted with a log-normal distribution: all distributions were fit with r2 > 0.8. From
these distributions, deposition was calculated for
each size interval (i) as:
dM i,down
ηdep,i =  1 – -------------------

dM
i,up
where dMi,down is the downstream and dMi,up is the
upstream interval mass associated with the lognormal fit.
Experiments
Table 1 lists the eight test conditions investigated.
A base condition was selected as: Re = 203 000; R0 =
5; construction = smooth; and orientation = horizontal-to-horizontal (H–H). Re of 203 000 was
achieved in a 0.152 m duct at an average velocity of
20.0 m/s. Given these conditions, Rep∞ ranged from
10 to 150, Stk ranged from 0.1 to 16, and De was
91 000. The base conditions were modified to evaluate how duct orientation, bend angle and bend
Fig. 1. Experimental set-up.
Table 1. Test conditions investigated
θ, degrees
Test description
Re (De)
Construction
Orientation
Basea
203 000
(91 000)
90
5
Smooth
H–H
Base + orientationa
203 000
(91 000)
90
5
Smooth
H–V
Base + bend angleb
203 000
(91 000)
180
5
Smooth
H–H
Base – bend anglec
203 000
(91 000)
45
5
Smooth
H–H
Base + constructiond
203 000
(91 000)
90
5
Gored
H–H
Base – constructione
203 000
(156 000)
90
1.7
Segmented
H–H
High Re, small R0f
368 000
(212 000)
90
3
Smooth
H–H
High Re, large R0g
368 000
(106 000)
90
12
Smooth
H–H
R0
Italic font identifies parameters that deviate from the base condition.
aH-P Products, Louisville, OH 44641; P/N EL-602-Z.
bTwo 90° bends as specified in footnote a butted together to form a 180° bend.
cH-P Products; P/N EL-601-Z.
dMcGill Airflow Corp., Groveport, Ohio 43125; Custom 5-piece, Gored, 6-in., 90° bend.
eMcMaster-Carr, Atlanta, GA 30374 ; P/N 1766K34.
fW.H. Brady, Inc., Elkton, MD 21922; P/N 90S, 8-in. diameter.
gH-P Products; P/N 14–800321-Z.
486
T. M. Peters and D. Leith
construction affect particle deposition. For the last
two conditions in Table 1, Re was 368 000 in a
0.203 m duct with an average velocity of 27.1 m/s.
All tests were conducted in a H–H orientation except
for one test, where the air entered the bend horizontally and exited vertically (H–V). Deposition by size
was measured three times for each test condition.
Figure 2 depicts the bend construction types investigated. Smooth bends (Fig. 2a) were manufactured
by bending straight tubing or fabricated by welding
together two stamped halves. The gored bend (Fig.
2b) was constructed by welding sections of sheet
metal together. The interior surface of the gored bend
deviated from a smooth bend in that: (i) the welded
seams protruded into the duct perpendicular to the
main direction of airflow; and (ii) the bend’s sectional
construction presented flat surfaces to the airflow.
The segmented bend (Fig. 2c) was joined by interlocking sheet-metal sections. Most segmented bends
have small R0; the bend tested in this work had an R0
of 1.7.
Statistical analysis
The combined data from the three runs for each test
condition were fitted with a cumulative log-normal
function (Cooper, 1982). The cutpoint (D50), or the
particle size associated with 50% deposition, and the
geometric standard deviation (GSD), a descriptor of
the shape of the deposition curve, were estimated
from the fitted function. The parameter estimates of
the fitted function were used to investigate the
similarity in deposition by size for different test
conditions.
RESULTS
Table 2 provides the fit r2 value, D50 and GSD for
each test condition. The cumulative log-normal
distribution explained >76% of the variability in the
experimental data for seven of the eight test conditions. The lowest r2 value (0.61) was observed for the
test with the segmented bend.
Figure 3 compares deposition by size for the base
condition (H–H orientation) to H–V orientation and
to model estimates from equations (1) and (2). The
deposition curve was slightly steeper in the H–H
orientation than in the H–V orientation (p = 0.001).
The deposition curves for both H–H and H–V orientations were shallower than those estimated with
either model. For particles <30 µm, the experimental
Table 2. Fit results
Test conditions
r2
Base
0.94
D50 (µm)
18.1
GSD
2.3
0.94
20.5
2.9
0.76
12.5
2.3
0.92
105.4
24.9
0.97
18.2
2.9
Base + orientation
H–V
Base + bend angle
θ = 180
Base – bend angle
θ = 45
Base + construction
Gored
Base – construction
0.61
39.5
2.7
High Re; small R0
Segmented; R0=1.7
0.88
21.4
3.0
High Re; large R0
0.80
19.5
3.7
Model comparison
For each test condition, experimental results were
compared with deposition estimated with the Pui et
al. (1987) model, equation (1), and the McFarland et
al. (1997) model, equation (2).
Fig. 2. Industrial bends and identification of key dimensions.
Fig. 3. Deposition by size: orientation varied.
Particle deposition in industrial bends
Fig. 4. Deposition by size: bend angle varied.
data overlapped with the Pui et al. (1987) model
estimates, but measured deposition was substantially
greater than that estimated with the McFarland et al.
(1997) model. For larger particles, measured deposition was substantially less than that estimated with
either model.
Figure 4 shows deposition by size as a function of
bend angle. For a given particle size, deposition
increased with bend angle. For θ = 45°, deposition
increased from 15% at 10 µm to 45% at 80 µm. For
larger bend angles, deposition neared 100% for 100 µm
particles.
Figure 5 presents deposition by size for bends of
different construction. Deposition in the smooth bend
was similar to that in the gored bend, but was
substantially and significantly higher than that in the
segmented bend. The deposition cutpoint for the
segmented bend (D50 = 39.5 µm) was significantly
larger than that for the smooth bend (18.1 µm, p <
0.001).
Figure 6 compares deposition by size measured in
bends with two curvature ratios to that estimated with
the models. Deposition measured in the tight bend
(R0 = 3) was statistically equivalent to that in the
gradual bend (R0 = 12): p = 0.53 for D50 values and
p = 0.23 for GSD values. Whereas the experimental
results compared favorably with the Pui et al. (1987)
model estimates for particles <30 µm, measured
deposition was greater than that estimated with the
McFarland et al. (1997) model. For particles >30 µm,
measured deposition was substantially lower than
that estimated with either model.
487
Fig. 5. Deposition by size: bend construction varied.
Fig. 6. Deposition by size: curvature ratio varied.
DISCUSSION
As shown in Figures 3 and 6, deposition by size in
industrial bends was not fully described by models
developed for small sampling tubes. Whereas the
experimental data in this work compared favorably
with the Pui et al. (1987) model estimates for particles <30 µm (Stk < 0.7), it was substantially lower
than that estimated for larger particles. Moreover, the
differences between measurement and models
became greater when the flow Reynolds number
488
T. M. Peters and D. Leith
increased from Re = 203 000 (Fig. 3) to Re = 368 000
(Fig. 6).
For relatively small particles, the agreement
between the deposition measured here and that estimated with the Pui et al. (1987) model illustrates the
importance of Stk in estimating deposition in bends.
Furthermore, the agreement suggests that deposition
is dominated by large-scale curvilinear motion as
opposed to the more subtle airflow features. The
region where models over-estimate deposition is
consistent with non-Stokesian drag effects and
airflow turbulence.
Some data associated with the smallest particle size
(near 10 µm) had relatively large error bars and did
not follow expected trends. For example, in Fig. 3,
the difference in deposition between orientations
should diminish as particle size becomes smaller and
gravity becomes less important; this trend was
observed for all but the smallest diameter particle
where the error bars were large. As discussed in
Peters and Leith (2003), the sedimentation pipette
was optimized to size large particles, and thus,
suffered from greater uncertainty for the smallest
particle size measured. The analysis technique might
be optimized for smaller particles, or perhaps more
practical, alternative real-time, in situ methods might
be used to determine deposition for particles of this
size and smaller.
Figure 7 compares Repr by particle size for the
current experiments to that used to build the models.
Repr was calculated as: Repr = DpVr/ν, where Vr is the
radial velocity of the particle. Vr was estimated from
a balance of outward centrifugal forces and drag
forces for a particle in the centerline of the bend. Plug
flow was assumed in this estimation. For the Pui et al.
(1987) and McFarland et al. (1997) data, Vr was
Fig. 7. Particle radial Reynolds number by size in this work and
the experimental work used to develop the models of
Pui (1987) and McFarland (1997).
estimated from conditions they reported. For conditions in the current work where Repr was less than
that of the models (i.e., Repr < 3 for particle sizes
<30 µm), the models acceptably represented drag
forces and experiments done here agreed with the
model estimates. However, as Repr progressively
became >3 (i.e. particles >30 µm), the models increasingly under-represented drag forces and overestimated deposition.
Airflow turbulence might also explain some model
over-estimates. Torobin and Gauvin (1961) showed
that free-stream turbulence decreases the critical
Reynolds number where the flow over a particle transitions from laminar to turbulent. Thus, drag forces
were further under-represented in the models. Crowe
et al. (1998) provided equations to account for this
behavior that might be useful in future modeling
efforts.
As shown in Fig. 3, the deposition curve for an H–
H oriented bend was steeper than that for an H–V
oriented bend. When oriented H–H, gravity caused
particles to settle throughout the length of the bend.
As gravitational settling is proportional to the square
of particle size, deposition in the H–H orientation
was greater than that in the H–V orientation for particles larger than ∼20 µm.
Theory predicts that particle penetration, P = 100%
– ηdep, is a multiplicative function of bend angle.
Thus, deposition in the 90° and 180° bends can be
estimated as 100% – P452 and 100% – P454, respectively. This relationship generally holds for particles
<20 µm, but not for larger particles (Fig. 4). As turbulent flow in a bend develops continuously, sufficient
curvilinear motion to deposit large particles was not
established by a bend angle of 45°. Better agreement
was observed between deposition measured in the
180° bend and that estimated as 100% – P902,
suggesting that most flow development had occurred
by a bend angle of 90°.
As shown in Figure 5, deposition by size was
nearly identical for the smooth and gored bends;
however, it was substantially lower and exhibited the
greatest variability in the segmented bend. Relatively
clean laboratory air might have leaked into the
segmented bend through its interlocking joints,
providing a clean air sheath at the bend walls that
reduced deposition. As the interior of the bend was
recoated with grease when sampling was switched
from the upstream to the downstream position, the
leaks through the interlocking joints might have
changed between runs, explaining the relatively high
variability in measurements for this test condition.
Alternatively, the segmented bend had a very tight
curvature ratio (R0 = 1.7) compared with the other
bends tested (R0 > 3). As noted by Tunstall and
Harvey (1968) and Rütten et al. (2001), drastically
different airflow patterns are anticipated in a tight
bend at these flow conditions due to flow separation
Particle deposition in industrial bends
at the inner wall; these differing airflow patterns may
account for reduced deposition.
For more gradual bends (3 < R0 < 12), deposition
by particle size was relatively unaffected by curvature ratio (Fig. 6). Deposition was slightly higher in
the gradual bend (R0 = 12) compared with that in the
tight bend (R0 = 3). Although estimates made with the
McFarland et al. (1997) model qualitatively agree
with this trend, the difference in estimated deposition
was greater than that observed in the experiments.
The major limitation of the present work was that
the inlet profiles were uniform in terms of the
velocity, particle size distribution, and particle
concentration. In industrial settings, deviations from
such uniform conditions often occur. More work is
required to evaluate how deposition changes as inlet
conditions become non-uniform.
CONCLUSIONS
This work explored particle deposition by particle
size in industrial duct bends. As the interior surface
of the duct bend was greased to prevent particle
bounce, the results are applicable to liquid drops and
solid particles where duct walls are sticky. These
experiments are the first of their kind for conditions
typical of industry. As such, they should be useful to
construct models appropriate for industrial conditions and to benchmark computer simulations.
A new model is required to describe droplet deposition in industrial bends adequately. The high radial
velocity that large droplets experience in industrial
bends represents a substantial departure from conditions in small diameter sampling lines, for which the
models of Pui et al. (1987) and McFarland et al.
(1997) were developed. Thus, these models underrepresent drag forces and over-estimate deposition in
industrial bends. Further, the current work suggests
that gravitational settling causes differences in deposition with orientation. Bend angle is important in
estimating deposition for particles >30 µm. In
contrast, curvature ratio is relatively unimportant for
R0 between 3 and 12.
NOMENCLATURE
a = duct radius
am, bm, cm, dm = constants used in the McFarland et
al. (1997) model
Cc = Cunningham slip correction factor
Dduct = duct diameter
down = downstream measurement
Dp = particle diameter
Dx = the particle diameter associated with x%
deposition
dM = differential mass
489
2
2
ρf U0
-----------Rb
Re- = ---------------De = Dean number = --------µf
R0
f = frequency of switching
GSD = geometric standard deviation =
D 84
-------D 16
H–H = horizontal-to-horizontal orientation
H–V = horizontal-to-vertical orientation
i = particle size interval
P = penetration
Py = penetration associated with a particle of
diameter y
R0 = curvature ratio = Rb/a
Rb = radius of bend
Re = flow Reynolds number = DductU0/ν
Rep∞ = free-stream particle Reynolds number =
DpU0/ν
Repr = radial particle Reynolds number = DpVr/ν
U0 = mean axial velocity upstream of the bend
up = upstream measurement
Vr = particle radial velocity
Sr = Strouhal number = 2fDduct/U0
Stk = particle Stokes number based on duct radius =
τU0/a
ηdep = percent of incoming particles that deposit
µf = fluid dynamic viscosity
ν = fluid kinematic viscosity
θ = bend angle
ρf = fluid density
ρp = particle density
τ = particle relaxation time = CcρpD2p/18µf
Acknowledgements—This work was made possible by a gift
from Ford Motor Company and the United Auto Workers to
support research in air engineering at the University of North
Carolina at Chapel Hill, by a Department of Education Fellowship for Interdisciplinary Training in Environmental
Engineering, and by a National Institute of Occupational Safety
and Health Educational Resource Center Training Grant
(T42/CCT410423–09).
REFERENCES
ACGIH. (1998) Industrial ventilation: a manual of recommended practice. Cincinnati, OH: American Conference of
Governmental Industrial Hygienists.
Alden JL, Kane JM. (1982) Design of industrial ventilation systems. New York: Industrial Press Inc.
Anwer M, So RMC, Lai YG. (1989) Perturbation by and recovery from bend curvature of a fully developed turbulent pipe
flow. Phys Fluids; 1: 1387–97.
Azzola J, Humphrey JAC, Iocovides H, Launder BE. (1986)
Developing turbulent flow in a u-bend of circular crosssection: measurement and computation. Trans ASME; 108:
214–21.
Baliff J, Greenburg L, Stern AC. (1948) Transport velocities
for industrial dusts. Am Ind Hyg Q; 9: 85–8.
Berger SA, Talbot L. (1983) Flow in curved pipes. Annu Rev
Fluid Mech; 15: 461–512.
490
T. M. Peters and D. Leith
Boersma BJ, Nieuwstadt FTM. (1996) Large-eddy simulation
of turbulent flow in a curved pipe. Trans ASME; 118: 248–
54.
Brockmann JE. (1993) Sampling and transport of aerosol. In
Willeke K and Baron PA, editors. Aerosol measurement:
principles, techniques, and applications. New York: Van
Nostrand Reinhold.
Brockmann JE. (2001) Sampling and transport of aerosol. In
Baron PA and Willeke K, editors. Aerosol measurement:
principles, techniques, and applications, 2nd edn. New York:
Van Nostrand Reinhold.
Cheng Y-S, Wang C-S. (1975) Inertial deposition of particles
in a bend. J Aerosol Sci; 6: 139–45.
Cheng Y-S, Wang C-S (1981) Motion of particles in bends of
circular pipes. Atmos Environ; 15: 301–6.
Cooper DW. (1982) On the products of lognormal and cumulative lognormal particle distributions. J Aerosol Sci; 13: 111–
20.
Crane RI, Evans RL. (1977) Inertial deposition of particles in a
bent pipe. J Aerosol Sci; 8: 161–170.
Crowe C, Sommerfeld M, Tsuji Y. (1998) Multiphase flows
with droplets and particles. New York: CRC Press.
DallaValle JM. (1932) Determining minimum air velocities for
exhaust systems. Heating, Piping Air Conditioning J; Sep:
639–41.
Enayet MM, Gibson MM, Taylor AMKP, Yianneskis M.
(1982) Laser-doppler measurements of laminar and turbulent flow in a pipe bend. Int J Heat Fluid Flow; Dec: 213–9.
Gregory WS, Martin RA, White BW, Nichols BD, Smith PR.
Leslie IH, Fenton DL, Gunaji MV, Blythe JP. (1991) Fires in
large scale ventilation systems. Nucl Eng Des; 125: 337–
345.
Hacker PT, Brun RJ, Boyd B. (1953) Impingement of droplets
in 90 degree elbows. NACA Technical Note No. 2999.
Cleveland, OH: Lewis Flight Propulsion Laboratory.
Hinds WC. (1999) Aerosol technology: properties, behavior,
and measurement of airborne particles. New York: John
Wiley & Sons.
Ito H. (1987) Flow in curved pipes. JSME Int J; 30: 543–52.
May DC, Berard DL. (1987) Fires and explosions associated
with aluminum dust from finishing operations. J Hazard
Mat; 17: 81–8.
McFarland AR, Gong H, Muyshondt A, Wente WB, Anand
NK. (1997) Aerosol deposition in bends with turbulent flow.
Environ Sci Technol; 31: 3371–7.
Peters TM, Leith D. (2003) Measurement of particle deposition
in industrial ducts. J Aerosol Sci; 35: 529–40.
Pui DYH, Romay-Novas F, Liu BYH. (1987) Experimental
study of particle deposition in bends of circular cross section.
Aerosol Sci Technol; 7: 301–15.
Rajahns GS, Thompkins RW. (1967) Critical velocities of mineral dusts. Can Mining J; Oct: 85–8.
Rowe M. (1970) Measurements and computations of flow in
pipe bends. J Fluid Mech; 43: 771–83.
Rütten F, Meinke M, Schröder W. (2001) Large-eddy simulations of 90° pipe bend flows. J Turbulence; 2: 1–14.
Silverman L, Billings CE, First MW. (1971) Particle size analysis in industrial hygiene. New York: Academic Press.
Tennekes H, Lumley JL. (1972) A first course in turbulence.
Cambridge, MA: MIT Press.
Torobin LB, Gauvin WH. (1961) The drag coefficients of single spheres moving in a steady and accelerated motion in a
turbulent fluid. AIChE J; 7: 615.
Tsai C-J, Pui DYH. (1990) Numerical study of particle deposition in bends of a circular cross-section-laminar flow regime.
Aerosol Sci Technol; 12: 813–31.
Tsai C-J, Pui DYH, Liu BYH. (1990) Capture and rebound of
small particles upon impact with solid surfaces. Aerosol Sci
Technol; 12: 497–507.
Tunstall MJ, Harvey JK. (1968) On the effect of a sharp bend in
a fully developed turbulent pipe-flow. J Fluid Mech 34: 595–
608.